Integrable Geodesic Flows on Two-Dimensional Surfaces (Monographs in Contemporary Mathematics) - Image 1

Price loading...

Springer Integrable Geodesic Flows on Two-Dimensional Surfaces (Monographs in Contemporary Mathematics)

Name: Integrable Geodesic Flows on Two-Dimensional Surfaces (Monographs in Contemporary Mathematics)
Brand: Springer

Geometry & Topology

Price History & Forecast

No Price Data Available

Price history will appear here once data is collected from Amazon.

Price Distribution

No price data available for histogram

Description

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object to be studied in our paper is the class of integrable geodesic flows on two-dimensional surfaces. There are many such flows on surfaces of small genus, in particular, on the sphere and torus. On the contrary, on surfaces of genus 9 > 1, no such flows exist in the analytical case. One of the most important and interesting problems consists in the classification of integrable flows up to different equivalence relations such as (1) an isometry, (2) the Liouville equivalence, (3) the trajectory equivalence (smooth and continuous), and (4) the geodesic equivalence. In recent years, a new technique was developed, which gives, in particular, a possibility to classify integrable geodesic flows up to these kinds of equivalences. This technique is presented in our paper, together with various applications. The first part of our book, namely, Chaps.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 1461369339
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Publication Date: 02 November 2012
Listed Since: 03 March 2013

Barcode

No barcode data available

Springer Integrable Geodesic Flows on Two-Dimensional Surfaces (Monographs in Contemporary Mathematics)

Price History & Forecast

No Price Data Available

Price Distribution

Description

Product Specifications

Barcode

Similar Products You Might Like

Integrable Geodesic Flows on Two-Dimensional Surfaces (Monographs in Contemporary Mathematics)

Integrable Hamiltonian Systems: Geometry, Topology, Classification

Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics (Mathematical Surveys & Monographs)

Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics)

Geometrical Dynamics of Complex Systems: A Unified Modelling Approach to Physics, Control, Biomechanics, Neurodynamics and Psycho-Socio-Economical ... and Automation: Science and Engineering, 31)

The Geometry of Higher-Order Hamilton Spaces: Applications to Hamiltonian Mechanics: 132 (Fundamental Theories of Physics, 132)

Geometrical Theory of Dynamical Systems and Fluid Flows (Advanced Series in Nonlinear Dynamics)

Analysis Of Harmonic Maps And Their Heat Flows, The

Geometrical Theory of Dynamical Systems and Fluid Flows (Advanced Series in Nonlinear Dynamics): 23

Riemannian Manifolds and Homogeneous Geodesics (Springer Monographs in Mathematics)

Riemannian Manifolds and Homogeneous Geodesics (Springer Monographs in Mathematics)

Geodesic Flows: 180 (Progress in Mathematics, 180)

Global Analysis: Differential Forms in Analysis, Geometry and Physics (Graduate Studies in Mathematics)

Springer - Three-Dimensional Flows: 53 Mathematics Survey

Springer - Three-Dimensional Flows: 53 Mathematics Series

Differential Galois Theory and Non-Integrability of Hamiltonian Systems (Modern Birkhäuser Classics)

Variational Problems in Geometry (Translations of Mathematical Monographs)

Translation Surfaces: 242 (Graduate Studies in Mathematics)

Translation Surfaces: 242 (Graduate Studies in Mathematics)

Morse Theory of Gradient Flows, Concavity and Complexity on Manifolds with Boundary

Nonlinear Analysis on Manifolds. Monge-Ampère Equations: 252 (Grundlehren der mathematischen Wissenschaften, 252)

Continuous Semigroups of Holomorphic Self-maps of the Unit Disc (Springer Monographs in Mathematics)

The Ricci Flow: Techniques and Applications: Geometric-analytic Aspects (Mathematical Surveys and Monographs): Part III: Geometric-Analytic Aspects

LECTURES ON THE GEOMETRY OF MANIFOLDS (2ND EDITION)